Retail sales dropped by 0.5 percent to a seasonally adjusted $87.16 billion last month, the Commerce Department reported yesterday, adding to the evidence that the economy continued to decline through the first quarter of this year.

The drop in sales followed a 2.6 percent increase in February. This rise was originally reported as 1.6 percent; however, much of the February increase was due to a rebound from a low figure in January when exceptionally cold weather kept consumers at home.

Commerce Secretary Malcolm Baldrige called yesterday's sales figures disappointing. He commented that "after seasonal adjustment, sales for the first quarter as a whole were about the same as in the quarter earlier, continuing the sluggish pattern of the past year."

In a separate report, the Federal Reserve Board yesterday said there was an increase of only $75 million in consumer installment credit in February. In January there was a $443 million gain in outstanding consumer credit.

High interest rates have discouraged consumers from going into debt to buy autos and other consumer durable goods. Yesterday's Fed report showed that installment credit increased at an annual rate of less than 0.5 percent, compared to a gain of 6.8 percent in this credit during 1981.

Most economists believe that the economy will only begin to recover after the income tax cuts due in July give a boost to personal spending. Reagan officials, who first said that the economy would turn around this spring, now expect recovery in the second half of the year, after the tax cuts come into effect.

The tax cuts and higher Social Security benefits due at midyear will together add "$45 billion at an annual rate to the income stream," Baldrige said. "This spending power will bolster retail sales and should be a critical factor influencing a recovery," he added.

However, persistent high interest rates throughout the recession have made analysts revise downward their projections for economic growth this year. Many fear that if there is no fall in rates, any recovery will be extremely weak and may be shortlived.

Company profits have been hard hit by the recession as firms have slashed prices to keep up sales. "Price promotions were heavy during the first quarter" of this year, Baldrige said. This, together with the poor sales volume, means that "profits probably declined further," he added.

Retail sales have climbed by only 1.2 percent in the last year, before accounting for inflation. In physical volume, after adjusting for price changes, sales are down over the year, the Commerce Department said.

One good sign from the March figures was an increase of 0.9 percent reported for sales of durable goods, which reached $26.99 billion. In the 12 months ending in March sales dropped by 2.2 percent, the report said. The February rebound in the total sales figures was led by a 5.7 percent jump in durable goods sales, which in turn was largely due to higher auto sales.